Cameras with a focal plane shutter have a "maximum sync speed" which cannot be exceeded when using studio flash units or other flash that is not able to "communicate" with the camera. The maximum sync speed is a function of the shutter design. There's no getting around this. The limitation is because of the design and operation of focal plane shutters.
Focal plane shutters are used in all Canon SLR cameras. Focal plane shutters have two blades or two curtains, depending on their design. At lower shutter speeds one shutter element (blade or curtain, depending on the design) will go completely across the film/sensor space, uncovering it completely and allowing light coming through the lens to impact the entire surface of the film or sensor. After the first shutter element has moved completely across the film/sensor space, then the second shutter element will start to move, again covering the film/sensor space and ending the exposure. The timing is based on the selected shutter speed.
As you go faster and faster with the shutter speed selection, there is a point reached (the "max sync speed") where the shutter elements cannot travel fast enough to fully expose the film/sensor and then start to close it off. At any faster shutter speed, the second shutter element will start to move before the first has completely uncovered the film/sensor. Thus, a slit - of varying width depending on the selected shutter speed - travels across the film/sensor space.
You cannot use an electronic flash - with its very fast timing - when the shutter speed is so fast that only a portion of the film/sensor is exposed at any one time. The "max sync speed" is the fastest shutter speed that has the film/sensor totally exposed to light coming through the lens.
Sometimes you will not be able to achieve sync with the shutter speed set at the advertised "max sync speed". This could be because of a lag in the triggering mechanism that fires the flash unit. Such lag is common in cheap radio slave systems.
The ability for some Canon Speedlites to operate in a "high speed sync" mode is based on a series of flash pulses emanating from the Speedlight over longer than normal flash pulse periods. You will get less effective light from the flash at any point in time, but it does allow for some creative flexibility in using the flash.