Groups, or "Send Tags" (a proprietary TextPower feature) are labels that you can use to tailor bulk message sends to a specific subset of an Opt-In list.
Groups can be any combination of letters and numbers, even spaces. If you are a utility, for example and want to be able to send a text message to everyone on a particular circuit you could assign all of the numbers that are associated with accounts that are along that circuit to a group (e.g., "Trunk Line 7). When a planned outage is scheduled and you want to inform everyone in that particular area about it you don't have to send a message to the entire list of numbers that have opted-in to receive updates - just send a message to that group.
Store codes are similar in function but can be used a bit differently. First, they are always numeric. A store code is just a special type of a send tag and it's used to make it easy for someone to Opt-In to a particular store in a chain - for example instead of texting just "pizza" they could text "pizza678" to designate that they are opting into the messaging services for store number 678 in a chain.
These groups, tags, labels or store codes - whatever you wish to call them - can be easily assigned when uploading a file or within AlertManager by individual numbers. See the other FAQs about how to assign these helpful tags to learn how to add them to your numbers.