After the founding of the PRC (i.e. the communists) in China, president Truman announced in 1950 that the US would keep their hands off any conflict between the communists and the nationalists, and that he will not defend Taiwan against a communist attack.
However, soon after that, the Korean War broke out, and the US stepped up on its anti-communism policy, making the nationalists in Taiwan an obvious ally. Truman sent the Seventh Fleet into the Taiwan Strait. Strategically, it was to help secure the southern supply routes to the Korean peninsula. In reality, it was as much to prevent the PRC from claiming Taiwan as it was to prevent the ROC from acting stupid and trying to retake China, making a mess of south-east Asia again.
In short, Truman was fed up with the Chinese civil war and gave a slap to both sides.
However, the tensions kept raising and finally, the nationalists decided to deploy troops on the remaining islands they still control along the Chinese coast, building defensive positions and digging in for the long term. This provoked the communists, and they mobilized their forces, determined to take Taiwan once and for all.
So in 1954, the communists attacked the remaining coastal islands that was still held by the nationalists and captured one of the islands. This is the start of what is now known as the First Taiwan Strait Crisis.
As the two sides showered each other with artillery, the nationalists managed to secure a mutual defense treaty with the US, that specifically did not apply to the coastal islands along China. The nationalists knew they could not hold off the large numbers that the communists throw at them, and agreed to back off in exchange for US protection of Taiwan.
The US threatened to use nuclear weapons on the PRC. In the end the PRC backed off.
And so started a 24-year long mutual defense treaty that officially put Taiwan under US military protection.
To summarize, the US was ready to ignore Taiwan, but circumstances changed, and Taiwan became a good anti-communist policy resource. During the time the mutual defense treaty was effective, the US would have (and was obligated to) provide military support to Taiwan in the case of a Chinese invasion. The treaty had specific limitations that made it apply to only the defense of Taiwan (and Pescadores).
The mutual defense tready was terminated in 1980, as the US established diplomatic relations with the PRC. And after that, came the Taiwan Relations Act.