What is technology in the Ricardo model?

this is attributed to better computer-production technology in the US. But what is that technology? Is it better physical capital, in the form of computer-building machines? Is it better human capital?

In a sense yes. For example, typical Cobb-Douglas function with capital labor and human capital would look like this:

$$Y = A K^{alpha} L^{beta} H^{1-alpha-beta} $$

Where A would be the technology that actually augments the production capabilities of the different factors ($K$ capital, $L$ labor and $H$ human capital).

You could have a technology that also augments just single factor, for example $ Y = K^{alpha} (A_LL)^{beta} H^{1-alpha-beta} $ or each factor could have its own separate technology. However, you should not confuse the technology with the stocks of capital, labor and human capital. This being said, you can consider $A$ as a factor that makes capital labor and human capital 'better'.

The technology here is considered in the loosest sense possible. For example, information technology such as skype or zoom allows people to give lecture online to large audiences making their stock of human capital more productive. Some idea about how to improve production process would also be considered. For example, if there are some teaching techniques that allow teacher to teach more efficiently that could be again considered a technology.

Most undergraduate textbook models will not explicitly include production functions in presentation of the Ricardian or Heckscher-Ohlin models, rather they will just assume that certain number of inputs just give you some outputs, but the production functions are included in more complex presentation of these models. See for example some graduate text such as Feenstra's Advanced International Trade.

Furthermore, the production function does not need to be necessary Cobb-Douglas, and it is not necessarily the most appropriate production function for the international trade models but it makes exposition of technology relatively easy so I used it as an example.

Is it related to TFP?

Yes it actually is the total factor productivity. The $A$ is also called the total factor productivity (see pp72 Bruda Wyplosz Macroeconomics). Also, the way how total factor productivity is measured is that people try to estimate the production function such as the one above by putting there all inputs in terms of capital, labor and so on and using that to actually estimate what is the effect of technology.