The box they gave you will be a router probably with an integrated modem. This could have four Ethernet ports for wired connections to computers, games consoles, etc. You also have a fifth connection to the router - your WiFi network.
Unlike Ethernet, WiFi can only pass one packet at a time. This might be a data packet from the router to one of the wireless connected devices, or it can be an acknowledgement packet going from a device to the router. Only one wireless device can be involved with a packet transfer at any time.
In contrast, Ethernet tend to connect to just one device, and can handle data packets in one direction while acknowledgement packets are simultaneously in the opposite direction. Each Ethernet can operate at the same time, and at the same time as single packets are going across the wireless network.
Wireless networks can operate in different modes - mode B had an instantaneous speed of just 11 Mbps; mode G reaches 54 Mbps; while mode N typically goes to 150 Mbps or faster. The wireless network speed will tend to drop to the speed of the slowest wireless device that is active on the network. Wireless networks can slow up when the channel starts to be heavily used especially by several different devices. There is no formal sequencing of which device can transmit, and if two or more devices start to transmit at the same time, then their transmissions will be corrupted, and neither device will know that there is a problem until some higher level software times out and initiates a recovery. Even a neighbour's wireless network can cause packer corruption if it is on the same channel. The further apart that devices are from the router, and from each other, the higher the chance of two transmissions colliding and corrupting each other.
If you are getting some interaction from a neighbour's network, log on to the router and try setting the wireless on a different channel. Try different channels to find the best one.
I hope this explains why you can be seeing problems.