mitkommen
to come along
To accompany someone who is going somewhere; to join a person or group on their way.
Wir gehen später noch ein Eis essen, willst du mitkommen?
We're going to get ice cream later; do you want to come along?

to come along / keep up
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to come along
To accompany someone who is going somewhere; to join a person or group on their way.
Wir gehen später noch ein Eis essen, willst du mitkommen?
We're going to get ice cream later; do you want to come along?

'Mitkommen' (to come along / keep up) is a separable verb. The prefix 'mit' comes at the end in a main clause, but remains attached to the verb in a subordinate clause. In the infinitive with 'zu', 'zu' goes in the middle.
Ich gehe ins Kino. Kommst du mit?
I'm going to the cinema. Are you coming along?
The meaning of 'mitkommen' (to come along / keep up) becomes clear from context. If it is about a place, it means literal accompaniment. If it is about a topic or an explanation, it means understanding. If it is about speed, it refers to the physical pace.
Die Erklärung war sehr schnell, aber ich glaube, ich bin mitgekommen.
The explanation was very fast, but I think I followed.
In the meaning 'begleiten' (to accompany), 'mitkommen' (to come along) is very often used as a question or as a direct request in the imperative to invite someone.
Wir gehen in den Park, komm doch einfach mit!
We're going to the park; just come along!
In the meaning 'verstehen' (to understand), the verb is very often negated. The expression 'ich komme nicht mit' (I can't follow) is a very common way to say that you don't understand something.
Kannst du das bitte wiederholen? Ich komme gerade gar nicht mit.
Could you please repeat that? I really can't follow right now.
to follow
'folgen' and 'mitkommen' overlap in two areas: movement and understanding. For movement, 'folgen' means that you go or drive behind someone. 'mitkommen' means that you join someone and go along with them. For understanding, you can 'folgen' an explanation or 'mitkommen' with an explanation. 'folgen' sounds a little more neutral here and focuses on the train of thought. 'mitkommen' often emphasizes whether the pace is too fast. The words can be confused because both can fit in lessons, conversations, and routes. So pay attention: behind someone = 'folgen'; joining in or keeping up = 'mitkommen'.

Im Mathekurs kommt er nicht mit, weil die Lehrerin sehr schnell spricht.
He can't keep up in the math course because the teacher speaks very quickly.
Herr Braun kann der Erklärung heute gut folgen.
Mr. Braun can follow the explanation well today.