For a list, under List Settings, Advanced Settings, Item-level Permissions, Edit Access, you can choose between:
- All Items
- Only their own
This setting applies to Delete Items and well as Edit Items permissions. So if you select Only their own, users can only edit and delete their own items, but cannot do anything to other users' items.
If you select None, then users with Edit Item or Delete Item permissions will still be unable to edit or delete any items. You are effectively overriding the permissions they already have for the list. This can come in handy if you have users' permissions set to include Edit Item for an entire site, but you want to restrict that for a specific list. This way you don't have to change permissions on the list (and thus stop inheriting the site's permissions, which can be bad if you ever change the site permissions - your customized list won't pick up those changed automatically!)
Of course if you have enough permissions on the list, you can still edit and delete items no matter the setting for Edit Access. I'm not sure what level, possibly Manage Lists or you may even need Full Control. I haven't tested this.
A good use for this is on a blog site where most users can only view posts, but you want them to be able to submit comments. You keep their site permissions as Read Item, then set their permissions on the Comments list to include Edit Item and Delete Item. (You can use the built-in Contribute permission level so you don't have to add specific permissions items.) You then set the Edit Access to Only their own so they cannot change other people's comments. (Unfortunately this breaks the Comments list's inheritance of permissions from the site, so be careful if you change the site permissions; you'll have the change the Comments list's permissions as well.)