We gather because we have an expectation that something is going to happen.
"Let us hold fast the confession of our hope without wavering, for he who promised is faithful. And let us consider how to stir up one another to love and good works, not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near." - Hebrews 10:23-25 ESV
Let me first say that one of the things that I love about being a believer is that it renders guilt and shame oriented obligation useless. Conviction is useful but guilt is foreign and abandoned. Jesus became my guilty one. My sins were put on Him. Guilt is never a means to gather because guilt is never a means period.
If you have been part of a play or complicated dramatic production what do you do as opening day gets closer? You gather together more and more to practice and prepare. Why? Is it guilt that draws you? No. It is desire. When that curtain goes up everything you have worked for will be presented to a group of people and that is exciting and scary and wonderful all at the same time.
'The Day' this passage in the book of Hebrews is talking about is the day of God's visitation.
When that curtain goes up the people see the actors and hear the music. Props are moved on cue and the things people are doing behind the scenes become visible to the spectators. At the same time the actors feel the audience and hear their applause. Both groups are seen and experienced by each other.
The same is true on God's day of visitation. God is there observing us and we are there observing Him. All of this is happening as something prepared beforehand is unfolding before us.
I don't want to be a person that has nothing to look forward to. I want to be a person that expects God to show up. God Is faithful. Since I know that to be true I always have something to look forward to. That manifests as a general air of expectation but it also manifests in specific expectations of divine appointments in scheduled gatherings.
If you have ever experienced a visitation of God then you know what it's like but if you haven't I'm not sure if I have the words to explain it. It is the most wonderful transcendent thing.
I don't want to miss it and grace removes all the barriers from us receiving all that God Is in those times. There is no guilt or shame there. God is there and we are in the best possible place to be for that moment in time.