You have your laptop connected to a Wi-Fi network with full bars. That's great. It's not the bars that matter though, but the actual speed of that connection. Here's a quick way to find how fast your computer's current Wi-Fi connection is and other information about that connection.
On a Mac, hold the Option key then click on the Wi-Fi icon at the top right area on the screen. A menu will appear: Under the current Wi-Fi network it shows a host of information about the current connection, including the IP addresses, MAC address, the Wi-Fi standard and the connection speed, which is shown as Tx Rate.
On a Windows computer, it's a bit more involved but still easy. First right-click on the Wi-Fi icon at the lower right corner area of the screen, then click on Open Network and Sharing Center.
Next, click on the Wi-Fi connection, which will open up the status window that shows you the current connection speed among other things. And then you can click on Details to find out about the IP address and other info.
The speed is generally shown in megabits per second. The speed tends to fluctuate, ranging from 20Mbps 450Mbps if the computer is connected to a wireless n (802.11n) network, and can get as high as 1,300Mbps for an 802.11ac network. However, the most important thing is if this number is higher than your broadband download speed, then you're likely getting the full internet speed on the computer. If it's lower, then it's definitely your Wi-Fi that's slowing down your connection to the internet.