Players not engaging

It's game time and the players are just sitting there spinning their wheels. They plan and what-if and weigh their odds and bicker in and out of character. Yeah, it's one of those sessions.

 What's happened?

1. The players might have insufficient information to make a decision. They may have forgotten some information. Perhaps one of your hints was inscrutable. The players might not see how some information they have aligns with one of their objectives.
   
2. The player characters might have unclear goals or clashing goals, or there might be disagreement in the group about which goal to pursue (due to differences in PC preference or differences in reasoning). They might be unclear about which goals should be prioritised above which others.
3. The players might have a real-life moral dilemma about acting to achieve in-character goals that don't align well with their own ideals, and are tip-toeing around having to confront that. This is a huge issue and is best served by halting the session to have the conversation.
4. You might have forgotten to give the player characters time pressure and stakes. There's a particular kind of malaise that can occur when you're using a subjective (or just subjective-feeling) experience/advancement system ('milestone' or 'narrative' or 'chapter' advancement) and you don't have a setting with big obvious time limits or opportunity costs or wandering damage. A feeling that the positive and negative consequences of action and inaction are all vague and distant can transition into a feeling that action and inaction don't really matter.
5. The players might be dreading that the wrong choice will endanger their PCs. This is a different way there can be a lack of motivation towards action over inaction. In this case, you've done such a good job as a GM getting the players invested in their characters and feeling the world has big dangerous stakes that they've become paralysed with indecision. Good work, bad outcome. I'm quite sad that I've never achieved this one. Probably the best way to coax things towards action is to remind them of how the world is ticking on in the background without them.
6. The players might be under the misapprehension that the GM should be deciding things for them. Apparently this can happen with novice players and/or due to 'learned helplessness' in the wake of unpleasantly railroady GM-ing. This is another huge issue where your best bet is to call a halt and discuss the problem in an understanding but matter-of-fact way.
7. The players might be too overloaded with information to make a good decision.

That last one's a joke. It might be possible to give the players 'too much' information but I've never seen it done (or even heard it complained about).

There are orthogonal mistakes, of course: giving the players too much false information from bad sources, giving the players too little likely-immediately-meaningful information, obfuscating information excessively, giving the players information in ways that makes it seem irrelevant, giving the players information that makes them regret their goals and objectives, giving the players information too fast for them to digest or note down, giving the players information after establishing a GM style in which nothing they learn ever really matters, etc.

Manage information to avoid a 'players not engaging' session

I have two tips here.

First

Establish PC goals early. Always summarise PC goals at the start of a session along with information you know they have which is likely to be relevant to those goals (and other key information). Constantly restate PC goals and key information during play, if even a glimmer of an opportunity presents itself. It's hard to overdo this. Remind PCs of their character motivations if those are substantially different from their immediate and long-term goals.

When the player (character)s acquire new information, try to frame it in terms of PC goals and other key information they already have, so that it slots neatly into their mental framework.

Second

When you're handing out any kind of information "X" via narration, you might have a tendency to hedge or use filler words. You absolutely must learn to overcome this. Cut out any qualifying language like this:

• "I guess it makes sense that X"
• "it's sort of X"
• "I suppose X would"
• "it's kind of... you know, X"
  
• "you think that maybe X"
• "[sigh and grimace] well... X"
• "Y! ...No, well actually, X"
  

Phrasing things this way undermines a player's trust in the quality, validity, and importance of the information content! It conveys, consciously or unconsciously, that the GM is uncertain about what's true in the world. It also conveys that the information wasn't important enough to pre-determine. And it conveys that the information wasn't connected enough to other things in the world for there to be an obvious answer.

Brains can only pay attention to so much, and are constantly filtering information into buckets based on its perceived usefulness. Hedging/filling will get information filtered disproportionately into the mental bucket with 'discard immediately' written on it.

The solution is just a matter of practice. Learn to pause and work out exactly what you want to say, then give a precise, confident, unambiguous answer. Even after a long pause you'll be much more likely to get information to stick in the players' heads.