Slowloris is a kind of Denial-of-Service attack in which the attacker tries to exhaust your server's resources by opening a lot of connections to it, but being extremely slow. Each open connection consumes some resources on your server: just a a bit of RAM for the connection buffers and socket state, but that's resources nonetheless.
mod_antiloris is a heuristic filter for such attacks. It tries to detect situations which are definitely fishy; in this case, when a single client (an IP address) has opened a lot of connections to your server and still has all of them in "READ" state, meaning that in the HTTP protocol, all these clients are supposed to talk next, but do not, or do it very slowly.
As with all heuristic tools, there is a trade-off: if the filter's threshold is too high, then an attacker may maintain a medium-scale attack while keeping under the radar. But if the threshold is too low, then you will begin to reject legitimate users. The main problem with mod_antiloris is that it works with IP addresses so it can be at odds with NAT: if a lot of distinct human users are connected on a single network which does NAT (e.g. 50 students from the same class, on a University network), then all their connections will appear, from your server, to come from the same IP address, and this may trigger mod_antiloris even though these clients would all be legitimate. Conversely, if the attacker is motivated enough to go distributed (launching the attack from a botnet, i.e. a lot of distinct hosts under his control), then mod_antiloris won't help, because this will look like a lot of distinct, legitimate clients.
In any case, I suggest that you leave this issue to the people who handle your hosting: this is best addressed at their level. You might want to investigate who could possibly have a grudge against you, but it is possible that the attack is non-malicious after all: a buggy scripted client software can have the same effect (although it would probably not appear as coming from two distinct IP addresses, one in Brasil and one in Indonesia).
