In Modern American bidding we follow the best practices of Standard American and 2/1 bidding. We open hands with 12-21 HCP and 5 or more cards in a major with 1 of that major.
It is in the responses to opening 1 of a major that Modern American shines as an improvement to Standard American and 2/1 bidding systems.
The weakness in 2/1 is the garbage bin bid of the Forcing 1NT. This bid collects all hands with 6-11 HCP that may or may not support the opening major suit bid. No wonder so many auctions go astray starting with that sequence. For Modern American, we prefer the using of the 1NT reponse to the opening major to match that of Standard American.
Responding 1NT means response has 6-9 HCP (tighter point range) and denies having 3 card support for the major. This allows the opener to make much better, sound decisions with their rebid (or pass).
The weakness in Standard American is the lack of a game forcing bid at a low level. In Modern Majors we will assign the response of 2♦ to be an artifical bid and game forcing. The responder may or may not holding diamonds, the 2♦ response shows 13+ HCP. It might or might not have support for the opening suit. There are a couple of exceptions, when a hand with Game Force values may bid something other than 2♦ as first reponse.
We still have a need to show hands stronger than 1NT would show (6-9HCP) and too weak to be game forcing (<13 HCP). To that end, we assign the response of 2♣ to showing those hands. 2♣ shows 11-12 HCP and may or may not have support for the opener. This is called the Extensile 2♣. It is very useful to cover these hand patterns/strength. We call the bid Extensile because we will stretch the bid meaning. We will also use the response of 2♣ when we have a game forcing hand AND a strong club suit. We use the 2♣ bid to preserve bidding room that bidding 2♦ would limit our bidding room.
Modern American Majors have more bidding improvments to respond to the opening major suit bid. You can read more elswhere on the website. See the Category Majors to read about Compressed Bergen, Splinter Bids, Unbalance Limit Raise and Balanced Game Raise conventions.