Multitenancy is a way of saying that you're not the only one using a piece of hardware. Cloud hosting providers use virtualization to achieve multitenancy and become more cost-efficient. Your virtual cloud server (hereafter referred to as a guest) is given a slice of the available resources (memory, CPU, etc). Since most guests won't make use of all their resources all the time it's common to do what's called over-provisioning - the allocation of more resources than available.
Let's assume we have a server with 8 CPU cores and 16 guests where each one is allocated a full CPU core. Most of the time this will be fine, but if all guests decide to max out their CPU at the same time they will only get access to 0.5 cores each. A worst case scenario is having another guest causing a lot of disk IO (for example through swapping) which might make your guest grind to a halt.
The hosting providers don't generally tell you how much they over-provision. It helps to be aware that over-provisioning exists and that the activity of others might affect your servers. Always have more capacity available than you need in case someone starts using a lot of the shared resources.
If you don't want to deal with multitenancy the only option is to go for dedicated servers. An interesting initiative from Rackspace is called OnMetal . It aims to give you the flexibility of cloud servers while using dedicated hardware. There's also whats called Hybrid Clouds  which allow you to have both cloud and dedicated servers in the same network.