esc_html() escapes a string so that it is not parsed as HTML. Characters like < are converted to <, for example. This will look the same to the reader, but it means that if the value being output is <script> then it won’t be interpreted by the browser as an actual script tag.
Use this function whenever the value being output should not contain HTML.
esc_attr() escapes a string so that it’s safe to use in an HTML attribute, like class="" for example. This prevents a value from breaking out of the HTML attribute. For example, if the value is "><script>alert();</script> and you tried to output it in an HTML attribute it would close the current HTML tag and open a script tag. This is unsafe. By escaping the value it won’t be able to close the HTML attribute and tag and output unsafe HTML.
Use this function when outputting a value inside an HTML attribute.
esc_url() escapes a string to make sure that it’s a valid URL.
Use this function when outputting a value inside an href="" or src="" attribute.
esc_textarea() escapes a value so that it’s safe to use in a <textarea> element. By escaping a value with this function it prevents a value being output inside a <textarea< from closing the <textarea> element and outputting its own HTML.
Use this function when outputting a value inside a <textarea> element.
esc_html() and esc_attr() also have versions ending in __(), _e() and _x(). These are for outputting translatable strings.
WordPress has functions, __(), _e() and _x(), for outputting text that can be translated. __() returns a translatable string, _e() echoes a translatable string, and _x() returns a translatable string with a given context. You’ve probably seen them before.
Since you can’t necessarily trust a translation file to contain safe values, using these functions when outputting a translatable string ensures that the strings being output can’t cause the same issue described above.
Use these functions when outputting translatable strings.