Block functions are functions of the form: {func} .. {/func}. In other words, they enclose a template block and operate on the contents of this block. Block functions take precedence over custom functions of the same name, that is, you cannot have both custom function {func} and block function {func}..{/func}.
By default your function implementation is called twice by Smarty: once for the opening tag, and once for the closing tag. (See $repeat below on how to change this.)
Only the opening tag of the block function may have attributes. All attributes passed to template functions from the template are contained in the $params variable as an associative array. The opening tag attributes are also accessible to your function when processing the closing tag.
The value of the $content variable depends on whether your function is called for the opening or closing tag. In case of the opening tag, it will be NULL, and in case of the closing tag it will be the contents of the template block. Note that the template block will have already been processed by Smarty, so all you will receive is the template output, not the template source.
The parameter $repeat is passed by reference to the function implementation and provides a possibility for it to control how many times the block is displayed. By default $repeat is TRUE at the first call of the block-function (the opening tag) and FALSE on all subsequent calls to the block function (the block's closing tag). Each time the function implementation returns with $repeat being TRUE, the contents between {func}...{/func} are evaluated and the function implementation is called again with the new block contents in the parameter $content.
If you have nested block functions, it's possible to find out what the parent block function is by accessing $smarty->_tag_stack variable. Just do a var_dump() on it and the structure should be apparent.
See also: register_block(), unregister_block().