Advance
Progress
When something advances and goes, it is moving forward. If you do this you will advance. You will progress.
しんこう
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
げんざい、六つのプロジェクトが進行中です。
Six projects are currently progressing.
おいしゃさんに、進行がんがあると言われました。
The doctor told me that I have advanced cancer.
フグエキスから作られた新しい薬がその病気の進行を抑えた。
The new drug made from Fugu extract has suppressed the progression of the disease.