as; in proportion to; with; as… then…
Expresses that one change happens in proportion to another change, like 'as X happens, Y happens'.
This pattern shows a natural, gradual connection between two changes. As one thing increases or progresses, the other changes accordingly. It often translates as 'as...' or 'with...'. For example, as you climb a mountain, the air gets thinner. The change is usually continuous and somewhat automatic, not a deliberate action.
It is commonly used in both spoken and written Japanese, but it sounds a bit formal, so in casual conversation, you might hear にしたがって or とともに, but につれて is still fine. The nuance is that both parts are changing, but the second part is a result of the first. It is not used for a single event, but for a process over time.
Note that the verb before につれて is in the dictionary form, not the past tense, because it describes a general trend or ongoing process. Also, the second part of the sentence often uses forms like ~ようになる, ~ていく, or adjectives to show change.