This adverb modifies the verb which immediately follows it.
「修飾する」という文法用語は modify です。
「副詞」は adverb
「動詞」は verb ですね。
そこで、「この副詞はすぐ後ろの動詞を修飾しています」は
This adverb modifies the verb which immediately follows it.
「すぐ後ろの」は「すぐ後ろに続く」= immediately follow を使って関係代名詞 which でつなぎました。
This adverb modifies the verb immediately following it.
「この副詞はすぐ後ろの動詞を修飾しています」は少しシンプルな言い方ならこのようにいいます:
This adverb modifies the verb right after it.
adverb = 副詞
verb = 動詞
modify = 修飾する
right after = 直後の
また、This adverb modifies the verb which immediately follows it.での関係代名詞のwhichを使わずに言うこともできます:
This adverb modifies the verb immediately following it.
ただし、whichを使わない時にfollowをfollowingに変えなければなりません。