What does input[[...]] do in a shiny observe event?

In the below code, I'm trying to understand what the input[[...]] in the two commented observeEvent() functions do. Could someone please explain?

I'm trying to adapt this code so the function of the individual delete action buttons rendered under each added table can be consolidated into a single selectInput() or selectizeInput() box, showing all tables available for deletion, and then I can remove these individual table delete buttons. I need to understand this input[[...]] part in the below code first, so perhaps I can do the equivalent with selectInput() or selectizeInput(). I've only used input$... before in referring to action buttons or other user input widgets for an observeEvent().

Code:

library(shiny)
library(rhandsontable)

data1 <- data.frame(row.names = c("A","B","C","Sum"),"Col 1"=c(1,1,0,2),check.names=FALSE)

ui <- fluidPage(
  br(),
  actionButton("addTbl","Add table"),
  br(),br(),
  tags$div(id = "placeholder",        
           tags$div(
             style = "display: inline-block", 
             rHandsontableOutput("hottable1")
           )
  )
)

server <- function(input, output, session) {
  uiTbl <- reactiveValues(div_01_tbl = data1) # mod
  rv <- reactiveValues()                
  
  observeEvent(input$hottable1, {uiTbl$div_01_tbl <- hot_to_r(input$hottable1)}) # mod
  
  output$hottable1 <- renderRHandsontable({rhandsontable(uiTbl$div_01_tbl, useTypes = TRUE)}) # mod
  
  observeEvent(input$addTbl, {
    divID <- paste0("div_", if(input$addTbl+1 < 10){"0"},input$addTbl+1) # mod
    dtID <- paste0(divID, "_DT")
    btnID <- paste0(divID, "_rmv")
    uiTbl[[paste0(divID,"_tbl")]] <- data1 # captures initial dataframe values
    
    insertUI(
      selector = "#placeholder",
      ui = tags$div(
        id = divID,
        style = "display:inline-block;",
        rHandsontableOutput(dtID), 
        actionButton(btnID, "Delete", class = "pull-left btn btn-danger"),
      )
    )
    
    output[[dtID]] <- renderRHandsontable({
      req(uiTbl[[paste0(divID,"_tbl")]])
      rhandsontable(uiTbl[[paste0(divID,"_tbl")]], useTypes = TRUE)
    })
    
    # print(btnID)
    
    # what does input[[dtID]] below do?
    observeEvent(input[[dtID]], {uiTbl[[paste0(divID,"_tbl")]] <- hot_to_r(input[[dtID]])})
    
    # what does input[[btnID]] below do?
    observeEvent(input[[btnID]],{
      removeUI(selector = paste0("#", divID))
      rv[[divID]] <- NULL
      uiTbl[[paste0(divID,"_tbl")]] <- NULL
    },
    ignoreInit = TRUE,
    once = TRUE
    )
  })
  
  
  observe({
    tables_list <- reactiveValuesToList(uiTbl)
    tables_list <- tables_list[order(names(tables_list))]
    table_lengths <- lengths(tables_list)
    cumsum_table_lengths <- cumsum(table_lengths)[table_lengths != 0L]
    
    for(i in seq_along(cumsum_table_lengths)){
      names(uiTbl[[names(cumsum_table_lengths[i])]]) <- paste("Col", cumsum_table_lengths[i])
    }
  })
}

shinyApp(ui, server)