Я бы сказал, что appointments - это скорее посещения, чем встречи.
Врядли можно сказать "договараиваюсь о встрече с врачом/парикмахером/..."

Appointment is an arrangement to meet someone at a particular time and place.
https://en.oxforddictionaries.com/definition/appointment

Elena, to make appointments is to call a medical professional for a time to be seen. I think this refers to MEETINGS.

What context would this be used in? The way I understand it, someone looks through their agenda and CONFIRMS MEETINGS that are on the books for that day/week, etc. Is that possible?

here it means to agree on/ schedule meetings with people

контекст, например
- приехал куда-то и договариваюсь о встречах с друзьями знакомыми, которых давно не видел
- договариваюсь о встречах с потенциальными клиентами/спонсорами/... - что-то предварительное, не очень формальное

Elena, an APPOINTMENT is when you call a professional such as a doctor or lawyer and ask them to look at their agenda and set aside a time slot to see you. A MEETING is when two or more people mutually agree to meet at a designated time and place - and doesn't necessarily have to be professional in nature.

confirm звучит как подтверждать что-то, о чем уже предварительно договорился

- having arrived somewhere, I ARRANGE TO MEET UP with friends and acquaintances who I haven't seen in ages
- I SET UP MEETINGS with potential clients/sponsors
both quite informal

Grumbler, I added CONFIRM before you explained the context. I removed it.

Ok, deleted, thanks)

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