Please tell me what is the difference between the following sentences
He celebrated a little early.
He celebrated a little too early.
It is a little late to do that thing.
It is a little too late to do that thing.
Early: sooner in time than on time (sooner than expected, desired, allowed, required, etc).
Too early: surpassing some threshold relative to being early.
We arrived early for the game, and we were able to find a great parking spot.
We arrived too early for the game: the gates to the stadium parking lot were still locked and we could not get in.
Ditto, for late.
Too can be used to indicate that something happened just before (or just after) the right or appropriate moment. It can also imply that something happened at an inappropriate or incorrect moment.
For 1., I can imagine that it his birthday soon. Maybe it is on Monday, but he has work on Monday, so he celebrated on Sunday instead. So, "He celebrated a little early." If someone said "He celebrated a little too early" in this scenario, then I feel like it might be the case that "this" a person believes that you can only celebrate exactly during the hours of Monday. So if he started celebrating at 11:50pm Sunday night, then "this" person would say he started celebrating too early. In other words, it was not the "right time" to celebrate, according to this person.
Another example would to imagine a man that is expecting to receive a promotion today. The boss is deciding between him and another person. The employee is so confident that he will get the promotion today that he took his friends out to celebrate the night before. His boss finally makes his decision and gives the promotion to the other person. So one might remark, "he celebrated too early". It implies that it was wrong of him to celebrate since he did not get the promotion. "He celebrated a little early" does not necessarily have the same implication. It is possible, but it would probably be implied by the speaker's tone rather than the words.
This can have a variety of meanings, in particular depending on the meaning of "late". I choose late to mean at night.
I can imagine two girls talking. It is nighttime. One friend wants to get ice cream. The other remarks "It is a little late to do that". It can suggest that it might dangerous to go at night.
If instead the friend says "It is a little too late to do that", it can suggest that the ice cream shop has closed. For example, she was trying to leave at 9:05pm, but the ice cream shop just closed at 9:00 pm. Again, 3. can imply 4., but this would be due to the speaker's tone, not his or her words.
In many social settings, there is a time where something needs to happen and a different time when people would like it to happens. For example, let's say you and a bunch of your friends are going on guided tour in a nearby city. To avoid everyone having to drive to the nearby city, you all agree to share rides. You decide to meet at a parking lot in your own city, leave some cars there, and all pile into a few cars to go to the tour. That saves a bunch of gas!
You all determine that, if you leave any later than 8:15, you will miss the guided tour. Everyone has to depart by 8:15. Knowing this, you all agree to meet up at 8:00 and have some coffee before hitting the road.
If someone arrives at 8:10, you might say "He arrived late." He didn't arrive at the planned time, but there was still time for him to make the tour. However, if someone arrives at 8:20, you might say "He arrived too late," because he has arrived so late that it is now impossible to go on the tour.
We use "early" and "too early" in the same way. Consider the game of baseball, where one person swings a wooden bat at a ball trying to hit it into the field. If you swing "too early," you'll miss the ball entirely. On the other hand, if you just swung "early" you may still hit the ball, but it may not go in the direction you intended because your swing is almost over before it hits the ball.
In addition to the general difference between "early/late" and "too early/late", sometimes "a little too" early/late is used ironically to mean "very much too" early/late.
Stranger: What an adorable baby! You'll have to fight the boys off with a stick!
Parent: She's only a week old, it's a little too early to worry about that.
Telemarketer: I'd like to speak to John Smith, please.
Family member: You're a little too late. We buried him last week.