What does the tilde (~) mean in my composer.json file?

Tilde means next significant release. In your case, it is equivalent to >= 2.0, < 3.0.

The full explanation is at Tilde Version Range docs page:

The ~ operator is best explained by example: ~1.2 is equivalent to >=1.2 <2.0.0, while ~1.2.3 is equivalent to >=1.2.3 <1.3.0.

Another way of looking at it is that using ~ specifies a minimum version, but allows the last digit specified to go up.

Seldeak's below comment is a simple sum up explanation of the Composer documentation.

Tilde operator is useful for the projects that version their libraries using semantic versioning scheme.

Semantic versioning is more of a guideline that evaluates to the next significant release.

For Composer, this operator means to allow minor releases (that can include patches) without allowing a major version (that may not be backward compatible) while installing and updating.

For example: ~4.1 will allow project versions >=4.1 but <5.0.

Credits: http://dwellupper.io/post/37/using-tilde-range-operator-to-resolve-dependency-version-in-composer-php

The tilde ~ is one of many constraints that can be used to handle versions.

Next Significant Release Operators (~, ^):

The ~ operator is best explained by example: ~1.2 is equivalent to >=1.2 <2.0.0, while ~1.2.3 is equivalent to >=1.2.3 <1.3.0

The ^ operator behaves very similarly, but it sticks closer to semantic versioning, and will always allow non-breaking updates. For example ^1.2.3 is equivalent to >=1.2.3 <2.0.0 as none of the releases until 2.0 should break backwards compatibility. For pre-1.0 versions it also acts with safety in mind and treats ^0.3 as >=0.3.0 <0.4.0

Hyphenated Version Range (-)

Inclusive set of versions. Partial versions on the right include are completed with a wildcard. For example 1.0 - 2.0 is equivalent to >=1.0.0 <2.1 as the 2.0 becomes 2.0.*. On the other hand 1.0.0 - 2.1.0 is equivalent to >=1.0.0 <=2.1.0

Wildcard Version Range (.*)

You can specify a pattern with a * wildcard. 1.0.* is the equivalent of >=1.0 <1.1

Simple Version Range (>, >=, <, <=, !=)

By using comparison operators you can specify ranges of valid versions. Valid operators are >, >=, <, <=, !=.

You can define multiple ranges. Ranges separated by a space ( ) or comma (,) will be treated as a logical AND. A double pipe (||) will be treated as a logical OR. AND has higher precedence than OR.

And finally Exact Version Constraint

You can specify the exact version of a package Example: 1.0.2