“Can you go gather some kindling?”
You're camping with your family. You want to start a camp fire, so you need some small sticks. You make this request of your son.
Can you go gather some kindling?
In casual speech, you say "go (do something)" to mean "go (somewhere) and (do something)". For example:
Do you want to go see a movie?
This means to go to a movie theater and watch a movie.
Could you go find me a screwdriver somewhere?
This means to go to the place where tools are kept and find a screwdriver for the speaker to use.
"Gathering" things means going somewhere, getting the things, and putting them all together in one place. Physical things that people "gather" include:
But it's actually more common to talk about gathering information. The idea is similar; you search in different places, find information, and put it all together. For example:
I did an Internet search and gathered some information about different models that we could go with.
We were able to gather names of over 50 different companies in the area that we can approach about advertising with us.
"Kindling" is small pieces of wood that you can use to start a fire. You start a fire by lighting the kindling on fire. Then, once the kindling is burning, you can add larger sticks and pieces of wood.