BankStack is the leading cause of things moving in your bags and bank.

It:

sorts your inventory, bank, or guild bank
fills incomplete stacks in your bank with items from your inventory
compresses your bags by filling incomplete stacks within them
puts a chicken in every pot, and pot in every chicken

Quick command reference:

/bankstack : show configuration
/sort : rearrange your bags
/sort bank : rearrange your bank
/sort account : rearrange your warband bank
/sort guild : rearrange your guild bank
/sort {group} : rearrange whatever group of bags you choose
/stack : fills stacks in your bank from your bags
/stack bank bags : fills stacks in your bags from your bank
/stack {group1} {group2} : fills stacks in group2 from group1
/compress : merges stacks in your bags
/compress bank : merges stacks in your bank
/compress {group} : merges stacks in group
/fill : fill empty slots in your bank from your bags
/fill {group1} {group2} : fill empty slots in group2 from group1
/squash {group} : fill up the front of the group, without sorting anything
/shuffle {group} : completely randomly rearrange the contents of this group

In the /bankstack configuration you'll find sections for "ignore" and "groups". Here's a bit of elaboration on the syntax for those parts.

You need, regrettably, to hear about bag ids first. Each bag has a number which addons use to interact with it.

Unfortunately, what number maps to what bag varies depending on game type. Take a look at https://warcraft.wiki.gg/wiki/BagID

The guild bank is a whole different system, and BankStack has made up the following fake bag ids for it: 51, 52, 53, 54, 55, 56, 57, 58

To ignore slot 1 of bag 0, the first slot in your backpack, go to the "ignore" panel and put "0 1" into the textfield and click "okay".

Groups are similar. Let's say that you're a herbalist, and only want to do some things to your herb bags.

You could put this into the "groups" textbox: herbs 3,4 Or this: bankherbs 10,11

You now have two custom groups, herbs and bankherbs. Presumably you keep massive herb bags in slots 3 and 4, and are making lots of money from this because you have the two most expensive bank slots as well (10 and 11).

Having created these groups you could:

/stack herbs bankherbs

Which would fill up stacks in your bank herb bags from stacks in your personal herb bags.

Predefined groups are: bank, bags, account, guild, all, and a few more.

Click the "list" button in the groups config to see a full list.