What exactly does 'since_id' and 'max_id' mean in the Twitter API

The max_id = top of tweets id list . since_id = bottom of tweets id list .

for more : get a deep look in the last diagram .. here

The max_id and since_id are used to prevent redundancy in the case of Twitter API calls. Visualize the tweets coming in as piling onto a stack. One API call has to specify how many (count) tweets will be processed. But as this call is made, new tweets may be added. In that case, if you draw out a stack and run through the process, you notice that there can be some 'fragmentation' or sections of unprocessed tweets stuck in between processed ones. This is visible in below image as well.

To get around this problem, two parameters are used to keep track of the latest/greatest ID tweet previously processed (since_id) and the oldest/lowest ID tweet recently processed (max_id). The since_id points to the bottom of the 'fragment' and the (max_id-1) points to the top of the 'fragment'. (Note that the max_id is inclusive unlike the since_id) So, the parameters together keep track of which part of the tweet stack still needs to be processed.

since_id and max_id are both very simple parameters you can use to limit what you get back from the API. From the docs:

since_id - Returns results with an ID greater than (that is, more recent than) the specified ID. There are limits to the number of Tweets which can be accessed through the API. If the limit of Tweets has occured since the since_id, the since_id will be forced to the oldest ID available. max_id - Returns results with an ID less than (that is, older than) or equal to the specified ID.

So, if you have a given tweet ID, you can search for older or newer tweets by using these two parameters.

count is even simpler -- it specifies a maximum number of tweets you want to get back, up to 200.

Unfortunately the API will not give you back exactly what you want -- you cannot specify a date/time when querying user_timeline -- although you can specify one when using the search API. Anyway, if you need to use user_timeline, then you will need to poll the API, gathering up tweets, figuring out if they match the parameters you desire, and then calculating your stats accordingly.