Volume vs Chapter
A chapter is one installment of a comic as first serialized; a volume is a book that collects several chapters, usually around eight to twelve for manga.
In depth
Manga is published first in chapters, in magazines or online, and then collected into numbered volumes. A volume typically gathers eight to twelve weekly chapters, so a series with three hundred chapters runs to around thirty volumes. American comics use issues instead of chapters, collected into trade paperbacks of five or six issues.
Why it matters
Recommendations online often refer to chapter numbers ("it gets good after chapter 50"). Dividing by roughly ten gives the volume. Anime adaptations usually cover a stated range of chapters, which tells a reader which volume to start from after watching.
Issues, chapters and arcs
In American comics the unit is the issue, published monthly, and issues are grouped into story arcs that become trade paperbacks. In manga the unit is the chapter, and volumes are simply consecutive blocks of chapters rather than story arcs, so a volume can end in the middle of a storyline. Webtoons use episodes, which are collected into print volumes later.
Extras between chapters
Manga volumes often add material not in the magazine: author's notes, sketches, bonus comics and character pages between chapters. Collected editions of American comics add covers, variant art and essays. These extras are one reason readers buy the volumes even after reading the chapters elsewhere.
What it means today
To continue a manga after an anime season, find the last chapter the season adapted and start from the volume that contains it.