Alignment

At its core alignment is a nine box system that can act as a shorthand between players and the DM as to how their player character is going to act in a general situation. 

So alignment is recorded on two scales: Lawful/Neutral/Chaotic and then Good/Neutral/Evil. As you can see there is a lot of scope within each box as you can put more emphasis on one of the words than the other. A LAWFUL Good character and a Lawful GOOD character would have different reactions to a situation. An interesting example of this happened to me as a player; a man approached the three party members trying to sell a helm of Long Ears (it's a thieves tool to increase perception) The Lawful Evil Drow tried to extort him as he was selling without a license. The LAWFUL good Knight wanted to take him to prison and the Lawful GOOD Squire offered to try and get him a job with the city watch in the armoury! 

For a player the alignment cuts to the very essence of their character, it informs their backstory and also acts as a filter for how they should act within the game. As such I find it a really useful tool for new players to use as they have something to reduce the infinite options available to them in social situations to a few alignment based options. Alignment also informs religiosity as there are Gods for each alignment such as Tyr who is Lawful Good and Lolth who is Chaotic Evil, if a character is a follower of a God then it follows that they would share alignment. 

As a DM alignment gives you the ability to throw moral conundrums at your players to see if their characters have changed and grown over the course of the adventure. These can be subtle tests of their faith or pranks played by chaotic Gods like Tymora. Also having a character act out of alignment can make for a very engaging session; the resulting fallout can have friendships called into question, the character can have a crisis of confidence and even lose faith. 

In my experience I have found that alignments should be fluid just like in real life. Experience can harden the heart but it can also spur a hero on to prevent history repeating itself. This leads me to a common complaint from gamers: Alignments feel like shackles. I can see where they come from but I also think that they are looking at the situation from a negative perspective. Alignment isn't a rigid box that you have to act within, it's how you act on average. If you aren't enjoying your alignment talk to the DM and have your character transition organically to the way you want to play, it'll give your group some fun role playing opportunities and a redemption storyline can be very rewarding.

Finally 5th edition tried to move away from alignments having rules implications, by this we mean that the alignment is only for the player not to be interacted with mechanically by the DM. This has changed a little since Tales From the Yawning Portal was released as there are some magic items that can only bestow their benefits upon characters of a certain alignment, these are hangovers from previous editions. If it is important to your table then it is something you can explore, I don't think the issue has ever come up overtly on any of my tables though.