Convenience stores are literally convenient in Japan, in my opinion.
24/7 open
Most of convenience stores in Japan are open 24/7. It is super nice!!!! You can go there whenever you want – like when you need to stay late at work, when you need to get some food midnight, when you need to wake up very early morning, etc.
What you can buy
Food
Food that you can eat right away, and also food that you can easily cook at home with microwave/pan.
Usually they would ask you if you want them to warm up your food, or you can find microwave you can use. Also you can find the electrical pot you an pour hot water.
Beverage
Water, juice, coffee, and also alcohol too. They will confirm you are not underaged at register.
You can find hot drinks in winter, frozen drink in summer, too.
Daily supplies
Shampoo/conditioner, face soap, a case for contact lens, tampons, sanitary pads, stationary such as notebook, pen, highlighter, sticky note, envelope for wedding/funeral, and so on.
Bathroom
You should ask them if you can use it or not, but mostly you can use it.
Some convenience stores especially around big train station or big city don’t have bathroom for customer.
ATM
Usually there is an ATM at convenience store. You can get cash and also put money on deposit as well.
Just noted that you might need to pay for transfer fee which depends on your bank or your status of bank.
Print(Scan & Copy) and FAX
Most of you wouldn’t buy a printer or a FAX machine especially you live alone and it could be short term.
You can use a printer for scanning or copying, and a fax machine for ¥1o to 50.
Payment
You can also pay tax, national health insurance, and etc at register at convenience store.
This is very easy and convenient, but you need to know that you cannot use your debit/credit card for some kinds of payments.
Buying ticket
Family mart, Seven Eleven, and Lawson have their own machine which you can buy the ticket for museum, concert, long distance bus ( including to the airport) and so on. Some services are not in English which might be difficult for you though.
Receiving your ordered package
Sometimes you want to get your package delivered to not your home, like you cannot receive it during available time, or you don’t have stable address, or you want to get it nearby your office, etc.
Some EC service like amazon japan, you can choose a convenience store as a place that you want your package delivered.
Just listed up what comes up on my mind, but a convenience store is very useful and helpful in Japan.
Let me know if you have any questions!