
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?

to follow
To be able to understand or follow something mentally or intellectually, especially during a fast explanation or a complex topic.
Der Dozent erklärt das so kompliziert, ich komme da überhaupt nicht mit.
The lecturer explains it so complicatedly; I can't follow at all.

to keep up
To be able to physically keep up with the pace of another person or group.
Ihr seid mir zu schnell, bei diesem Tempo komme ich nicht mit.
You're too fast for me; I can't keep up at this pace.
'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
Both words can express that you understand an explanation. „Folgen“ generally refers to understanding and following someone's thoughts and arguments, while „mitkommen“ particularly emphasizes keeping up mentally with a fast or difficult explanation. „Folgen“ often fits the progression of an argument, while „mitkommen“ is suitable when the pace is fast.

Bei deiner schnellen Erklärung komme ich gedanklich kaum mit.
I can barely keep up mentally with your fast explanation.
Ich kann deiner Erklärung gut folgen, weil die Argumente klar geordnet sind.
I can follow your explanation easily because the arguments are clearly organized.